It's Zenith Infotech. They are a managed services provider, a legitimate company.
What happened to me is that I browsed their website, and they called about ten minutes later, leaving a voicemail saying they are following up to see if I had any questions! I did not fill in any web forms either. Maybe they did a reverse IP lookup and found my business name.
They just called again. They do identify themselves, and they're a legitimate company that some of my IT colleagues use with great success, so it's not like they're scammers. They just have weird marketing techniques, to put it nicely. The sales guy who called just said "someone from your company left a message for us!" I told him that's not true, and described what I had observed on June 18 (see above), and he said he would "close the lead."